Nuclear magnetic logging tools, such as disclosed in U.S. Pat. Nos. 4,933,638 to Kenyon et al. for "Borehole Measurement of NMR Characteristics of Earth Formations, and Interpretations Thereof"; and 5,055,787 and 5,055,788 both to Kleinberg et al. for "Borehole Measurement of NMR Characteristics of Earth Formations", measure the number and nuclear magnetic resonance (NMR) relaxation rates of hydrogen atoms in the pore space of rocks by measuring the amplitude and decay rate of signals resulting from pulse-echo sequences. In essence, the nuclear magnetic logging tools send a stream of RF-pulses into the formation and monitor the returning pulses which are called spin echoes. The measurements made are typically cyclical, with each cycle taking several seconds. Interpretation algorithms are then used to find the formation properties of interest.
The signal measured by a nuclear magnetic logging tool, such as the Pulsed Nuclear Magnetism Tool (PNMT, mark of Schlumberger) is proportional to the mean density of hydrogen nuclei in the fluid that occupies the pore-space. Hydrogen nuclei in the rock matrix relax too rapidly and are not detected by the tool. Since the hydrogen density in water and liquid hydrocarbons are approximately constant, the detected signal can be calibrated to give the volume fraction of the fluid occupying the pore space.
NMR relaxation of a water saturated porous rock is not a simple exponential relaxation, but it is a continuous superposition of exponential relaxations. For example, in an inversion-recovery experiment, the signal obtained after an inversion and a recovery time of length t is ##EQU1##
Loosely speaking, a(T.sub.1)dT.sub.1 is the volume fraction of the fluid whose relaxation time is between T.sub.1 and T.sub.1 +dT.sub.1, where T.sub.1 is spin-lattice relaxation time. This interpretation is only approximately correct because any isolated pan of the pore-space has a multi-exponential relaxation [1]. However, pores of rocks are in a fast diffusion regime where the signal is approximately single-exponential, and the relaxation time is proportional to the volume to surface ratio. Several researchers have demonstrated for water saturated sandstones that the pore size distribution is closely related to the distribution of NMR relaxation times [2-4].
Short relaxations times are due to water that is bound to clay minerals or water in pores that are too small to be flushed by a feasible pressure gradient. Also, heavy (viscous) hydrocarbons have shorter relaxation times. Fluids that relax slowly have low viscosity and reside in large pores. Hence, the slowly relaxing fluids can be produced provided there is sufficient permeability. It is therefore important to quantify the volume of the slowly relaxing fluids.